Hair particles breaks in half - blender cycles
To see if we are on the same page, here is my broken hair:



If that is what you are seeing -- and it looks similar -- here are ideas/options: 

Have you tried using the B-spline checkbox under the Particle System's Render  area? Also choose a higher "Steps" settings -- although doing so increases render time... But see if that addresses the issue. 

In the same vein, see if using Curve Segments as primitives (this is under the Particle Systems "Cycles Rendering" area) helps. Turn on cull back-faces and  turn curve subdivisions to 4 or 5 or 6.

For comparison:



The image above is without B Splines and with primitives set to Line segments. My hairs break at the first crinkle... perhaps that is what you are seeing?



Above: Same as first image, but with B Splines on and Steps set to 5.


Above: Same as first image, but with (B splines not on) and Primitives set to Curve segments.